Question: Solve for $x$ : $5x^2 + 10x - 315 = 0$
Dividing both sides by $5$ gives: $ x^2 + {2}x {-63} = 0 $ The coefficient on the $x$ term is $2$ and the constant term is $-63$ , so we need to find two numbers that add up to $2$ and multiply to $-63$ The two numbers $9$ and $-7$ satisfy both conditions: $ {9} + {-7} = {2} $ $ {9} \times {-7} = {-63} $ $(x + {9}) (x {-7}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 9) (x -7) = 0$ $x + 9 = 0$ or $x - 7 = 0$ Thus, $x = -9$ and $x = 7$ are the solutions.